This study develops an iterative dual BEM (Boundary Element Method) model for oblique wave interaction with breakwaters having perforated thin plates. A quadratic pressure drop condition is imposed on the perforated plates and the dual BEM model can consider the effect of wave height on the wave energy dissipation by perforated plates directly. The numerical method to solve the kernel function integrals generated from the hypersingular boundary integral equation has also been developed by introducing suitable parametric equations. The effect of evanescent wave modes is included in the iterative dual BEM model, which can decrease the total element numbers and improve the computation efficiency significantly. Besides, an iterative analytical model for oblique wave interaction with single vertical perforated barrier is developed, and the excellent agreement with the dual BEM solution validates the correctness of the iterative dual BEM model. The present iterative dual BEM model can be further used to analyze the hydrodynamic performance of breakwaters with perforated thin plates in arbitrary shapes.
Breakwaters having perforated thin plates like Jarlan-type breakwater, perforated barriers and perforated semi-circular breakwaters have been often used in practical engineering, as the perforated plates can dissipate wave energy and reduce wave forces on the structures effectively (Okubo et al., 1994; Zhang et al., 2005; Shepsis et al., 2007). Besides, the perforated plate could be an effective wave absorber by attaching it to a vertical wall and has been well applied (Wu et al., 1998; Cho and Kim, 2008). Due to the various sea conditions in different engineering locations, a reliable and high-efficiency method to predict the hydrodynamic performance of breakwaters having perforated thin plates should be very important for practical engineering design.
Many studies on wave interaction with breakwaters having perforated plates have been conducted based on potential theory, which can estimate the hydrodynamic characteristics of breakwaters reasonably and rapidly. The common methods are analytical solution (e.g., Isaacson et al., 1998; Li et al., 2003; Liu and Li, 2012) and BEM (e.g., Koley and Sahoo, 2017; Liu and Li, 2017; Vijay et al., 2019). Analytical solutions are quite timesaving but usually need complicated derivations and only deal with perforated plate breakwaters with typical shapes, which leads to limits for practical engineering application. Multi-domain BEM can well consider the degenerate boundary problem by introducing artificial boundary and dividing the computation region into multiple domains. Then the integral equation is discretized independently in each domain and combined on common boundary, and the unknown variables can be determined by solving simultaneous equations connected from different domains. However, the way to divide the computation region can be quite different with regard to different shapes of perforated plate breakwaters. By introducing a hypersingular integral equation into the conventional BEM, dual BEM can build numerical model without setting artificial sub-domains near the thin plate (Chen et al., 2002; Chen et al., 2004; Yueh et al., 2016). Combining the advantage that BEM can consider perforated plate breakwaters with complicated shapes, dual BEM should be quite suitable for analyzing wave interaction with breakwaters having perforated plates both in the research and practical application.